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How to find the slope of a line.

The slope of a line characterizes the general direction in which a line points.  To findthe slope, you divide the difference of the y-coordinates of a point on a line by the difference of the x-coordinates.

Slope of vertical and horizontal lines


  • The slope of a vertical line is undefined

    . This is because any vertical line has a x or "run" of zero. Whenever zero is the denominator of the fraction in this case of the fraction representing the slope of a line, the fraction is undefined
  • The slope of a horizontal line is zero
    . This is because any horizontal line has a . Y or "rise" of zero. Therefore, regardless of what the run is (provided its' not also zero!), the fraction representing slope has a zero in its numerator. Therefore, the slope must evaluate to zero.
This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line
Interactive slope |Interactive Linear Equation
Related pages: slope intercept form of a line | Erroneous Slope
Worksheet on Slope Of A Line

 Formula to find the slope of a line  

Formula for the slope of a line
    Example 1of the Slope of A line
  • The slope of a line through the points (1, 2) and (2, 5) is 3 because every time that the line moves up three (the change in y or the rise) the line moves to the right (the run) by 1.
    • Picture of the slope of a line
    Illustrated Example Two
  • The slope of a line going through the point (1,2) and the point (4,3) is 1/3.
    • Graph of the slope of a line
There is a fundamental point to remember about calculating slope.
  • Every line has a consistent slope. In other words, the slope of a line never changes. This fundamental idea means that you can choose ANY two points on a line to find the slope. This should intuitively make sense with your own understanding of a straight line. After all, if the slope of a line could change, then it would be a zigzag line and not a straight line.
This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line

Interactive Slope


Click and drag around either of the points below, as you move the points around, you can see the line's slope will adjust accordingly.
This Page: Do any two points determine the slope of a line? | Practice Problems | Slope of Vertical a Line | Slope of Horizontal Line
Practice Problems
Find the slope of A line Given Two Points

Practice Problem 5) What is the slope of a line that goes through the points (10,3) and (7 , 9) ?

 Answer 


Practice Problem 6) A line passes through (4, -2) and (4 , 3). What is its slope?

 Answer 



Practice Problem 7) A line passes through (2, 10) and (8 , 7). What is its slope?

 Answer 


Practice Problem 8) A line passes through (7,3) and (8 , 5). What is its slope?

 Answer 


Practice Problem 9) A line passes through (12,11) and (9 , 5). What is its slope?

 Answer 



Practice Problem 10) What is the slope of a line that goes through (4, 2) and (4, 5)?

 Answer 

Slope Practice -- Problem Generator

You can practice solving this sort of problem as much as you would like with the slope problem generator below. It will randomly generate numbers and ask for the slope of the line through those two points. You can chose how large the numbers will be by adjusting the difficulty level.



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